Computing with Analyzed Shapes
Shapes play an important role in many human activities, but are rarely seen in their natural form as raw and unanalyzed. Shapes are usually analyzed or structured in terms of their certain parts. Analyzed shapes or shape decompositions are central to this paper. Different shape decompositions are developed together with their algebras. The most interesting decompositions are the ones that could successfully be used as shape approximations. Two kinds of such decompositions: discrete and bounded are examined in greater detail.
KeywordsEquivalence Class Minimal Element Analyze Shape Spatial Object Shape Part
Unable to display preview. Download preview PDF.
- Birkhoff, G: 1993, Lattice Theory, American Mathematical Society, Providence, Rhode Island.Google Scholar
- Gratzer, G: 1979, Universal Algebra, American Mathematical Society, Providence, Rhode Island.Google Scholar
- Gratzer, G and Whitney, S: 1978, Infinitary varieties of structures closed under the formation of complex structures (Abstract), Notices American Mathematical Society 25: A–224.Google Scholar
- Krstic, D: 1996, Decompositions of Shapes PhD thesis, University of California Los Angeles.Google Scholar
- Stiny, G: 2001, How to calculate with shapes, in EK Antonson and J Cagan (eds), Formal Engineering Design Synthesis, Cambridge University Press, Cambridge, pp. 24–60.Google Scholar
- Stiny, G: 1980, Introduction to shape and shape grammars, Environment and Planning B 7: 243–251.Google Scholar